Measurement of Length and Motion

Deepa's friends recall people measuring with body parts: Hardeep's grandmother measures cloth by the length of her arm; farmers count strides to divide fields into beds; some use the length of their feet. Deepa's mother uses the handspan, which she calls balisht.

The five friends measure the same table with their handspans:

The numbers differ because their handspans are of different sizes. The handspan here is a unit, and a length is expressed in two parts — a number and a unit (13 handspans: 13 is the number, handspan the unit).

India has a rich history of measurement. Angula (finger width), multiples of angula, dhanusa and yojana are units mentioned in ancient Indian literature, used for measuring artefacts, architecture and town planning. The angula is still used by traditional craftspeople such as carpenters and tailors. Objects with ruled markings that could be scales have been excavated from sites of the Harappan Civilisation.

Different systems of units grew up in different places. When people travelled, this caused confusion, so countries came together and adopted standard units: the International System of Units (SI units).

• The SI unit of length is the metre, symbol m.
• 1 m is divided into 100 equal divisions, each a centimetre (cm).
• On a 15-cm scale, each centimetre is divided into 10 equal parts, each a millimetre (mm). 1 mm is the smallest length you can measure with it; 1 mm = 0.1 cm.
• For large lengths we use the kilometre (km) = 1000 m.

  1 km = 1000 m      1 m = 100 cm      1 cm = 10 mm

1. Choose an appropriate scale — 15-cm scale for a pencil; metre scale or measuring tape for a room's height; a flexible tape (tailor's tape) for the girth of a tree or your chest.
2. Place the scale in contact with the object along its length (Fig. 5.4).
3. Keep your eye directly above the point being read — e.g. directly above the tip of the pencil (position B in Fig. 5.5). Looking from the side gives a wrong reading.
4. Broken scale / unclear zero: start from any other full mark, say 1.0 cm, and subtract that reading from the reading at the other end.

• Unit names (kilometre, metre, centimetre, millimetre) begin with a lowercase letter, except at the start of a sentence.
• Symbols km, m, cm, mm are lowercase and are never followed by 's' for the plural.
• No full stop after the symbol, except at the end of a sentence.
• Always leave a space between the number and the unit — "15 cm", not "15cm".

Activity 5.1: measure a comb, pen, pencil and eraser with a metre scale, always writing the number and the unit, and compare with friends' measurements.

Anish's family put string lights along the arches of their verandah — how much would they need? For a curved line, use a flexible measuring tape, or lay a thread along the curve, mark it, then straighten the thread and measure it with a metre scale (Fig. 5.8).

Going to a garden for a class visit, the friends disagree about whether the garden or the school is closer: Tasneem and Padma say the garden, Deepa and Anish say the school, Hardeep says about equal. All of them are correct — each is measuring from a different house. If they had all measured from one point, such as the bus stand, their answers would agree.

When distance is stated with respect to a fixed object or point, that point is called a reference point.

• Kabaddi court: before drawing lines with chuna (limestone powder), Deepa says they must first fix a reference point to measure from.
• Kilometre stones: on the way to Delhi, Padma reads "Delhi 70 km", then "Delhi 60 km". Delhi is the reference point; her position is 70 km, then 60 km from it — it is changing with time.

An object is said to be in motion if its position changes with respect to the reference point with time. If it does not change its position with respect to the reference point with time, it is at rest.

Deepa on the bus: passengers stay in their seats — compared with herself or the bus, they are at rest. Compared with a building outside, they (and the bus) are in motion.

An object is placed with one end at the 1.0 cm mark; the other end is at 10.4 cm.

Solution:

1. Length = reading at far end − reading at starting end
2. = 10.4 cm − 1.0 cm
3. = 9.4 cm

The distance between school and home is 1.5 km. Express it in metres.

Solution:

1. 1 km = 1000 m
2. 1.5 km = 1.5 × 1000 m
3. = 1500 m

A friend's height is 1.42 m. Express it in cm and mm.

Solution:

1. 1 m = 100 cm → 1.42 m = 1.42 × 100 = 142 cm
2. 1 cm = 10 mm → 142 cm = 142 × 10 = 1420 mm

A wheel's outer boundary measures 2 m (using a string). The wheel turns 50 times.

Solution: distance = boundary × number of turns = 2 m × 50 = 100 m. A device called a Jones Counter uses this idea to measure road-race distances.

Measure a comb, pen, pencil and eraser with a metre scale; record in Table 5.2 with number and unit; compare with friends and discuss reasons for small differences.

List five objects in motion and five at rest (Table 5.3) with a justification — e.g. a cow grazing in the field (motion), a tree (rest).

Drop an eraser from a height and watch it fall in a straight line — like a falling orange, a march-past, or a pushed box: linear motion.

Tie an eraser (or potato) to a thread and whirl it — it moves in a circle, like a merry-go-round: circular motion.

Hang the eraser by the thread, pull it slightly to one side and release — it moves to and fro like a swing: oscillatory motion.

Press one end of a thin metal strip (about 50 cm long) to a table with books or a brick; press the free end and release — it moves up and down: oscillatory motion.

In a children's park (Fig. 5.18), classify motions as linear, circular or oscillatory in Table 5.4 — e.g. a swing moving to and fro is oscillatory; a slide is linear; a merry-go-round is circular.

Deepa at a cloth shop (shopkeeper with a metal measuring rod) and at the tailor's (flexible measuring tape).

Deepa, Padma, Tasneem, Anish and Hardeep measuring the classroom table with their handspans.

A metre scale; a 15-cm scale marked 0–15 cm, each centimetre divided into 10 millimetre divisions.

(a) Correct — scale in contact with the object along its length; (b) incorrect — scale tilted away from the object.

Three eye positions A, B and C looking at a pencil tip against a scale; B (directly above) is correct.

An object measured from the 1.0 cm mark to 10.4 cm — length 9.4 cm.

A house with string lights on verandah arches; a thread laid along a curved line, then straightened and measured with a scale.

A map strip showing the bus stand, school, Deepa's, Anish's, Hardeep's, Tasneem's and Padma's houses, and the garden.

A long measuring tape; children drawing Kabaddi-court lines from a marked reference point.

A kilometre stone reading "Delhi 70 km"; a diagram of stones at 70 km and 60 km with Delhi as the reference point.

A box pushed in a straight line (linear); an eraser whirled on a thread (circular); a hanging eraser swinging (oscillatory); a metal strip vibrating at a table edge (oscillatory).

A park with swings, a slide, a merry-go-round and other rides showing different types of motion.

A track that slopes straight down from the top, goes round a vertical loop, and runs out straight to the end, with points A–F marked along it.

1. Match the lengths with suitable units: distance between Delhi and Lucknow; thickness of a coin; length of an eraser; length of school ground — centimetre, kilometre, metre, millimetre.
2. True or False: (i) A car moving on a straight road is an example of linear motion. (ii) Any object changing its position with respect to a reference point with time is in motion. (iii) 1 km = 100 cm.
3. Which is not a standard unit of length? (i) millimetre (ii) centimetre (iii) kilometre (iv) handspan
4. Find the smallest value that can be measured by different scales and tapes at home and school; tabulate.
5. The distance between your school and home is 1.5 km. Express it in metres.
6. Measure the length of the curved part of the base of a tumbler or bottle.
7. Measure your friend's height and express it in metres, centimetres and millimetres.
8. Estimate how many coins placed end to end cover one side of a notebook; verify by measuring with a 15-cm scale.
9. Give two examples each of linear, circular and oscillatory motion.
10. List three objects each whose lengths are easiest to express in mm, in cm and in m (Table 5.6).
11. A ball starts at A on a rollercoaster track (Fig. 5.19) and escapes through F. Identify the types of motion and the corresponding portions of the track.
12. Tasneem wants to make a metre scale. Of plywood, paper, cloth, stretchable rubber and steel, which should she not use, and why?
13. Design a card game on conversion of units of length.

Worked answers to the textbook questions are in the Question Bank (section G).

1. Are the tape and rod similar to the scale in a geometry box? What did mother mean by char angula?
2. Why were the numbers of handspans different for each friend?
3. Would it be convenient to use the metre for the distance between two cities or the thickness of a page?
4. If we all measure the table again with a metre scale, will our results still differ?
5. Why are some length-measuring devices made of flexible materials?
6. How would Anish's family have measured the length of string lights for the arches?
7. What do kilometre stones indicate? How could Padma tell she was getting closer?
8. When does the position of an object change with respect to a reference point?
9. On a windowless ship moving steadily in a straight line on a calm sea, can you tell if it is moving?
10. Is the motion of a whirled eraser the same as a merry-go-round? Is a hanging eraser's motion like a swing?

• Find the thickness of a single page of a notebook using a scale; describe your method and result.
• Measure length and breadth of fallen leaves from one tree (Table 5.7); discuss why they vary.
• Ask elders about old units of length; find out about length scales from archaeological sites in India.
• Create a maze using lines of 1 cm, 2 cm and combinations.
• Mark your height on a wall every three months to keep a height record.
• Measure distance with a bicycle wheel: count turns and multiply by the wheel's boundary length; find out about the Jones Counter.